C 761 ] 
regarded, as having no efifedt at all in the refult. 
For if in that part a ~ — ^ of the value of S\ 
above exhibited, in which the firfl terms, a and bx^ 
enter, there be fubfHtuted px, qx , rx, fucceffively, 
for x (according to the prefcript) the fum of the 
quantities thence ariling will be 
a 
f- x 1 
b 
a 
fx 1 
a 
r x 
p x qx 
which, becaufe p z = 1, q z — 1, &c. (or p- 
cr = f } &c.) may be expreffed thus ; 
1 
? > 
a - — . j 
x p + q + 
XX r 1 J 
h - ? . 2 
— 7 x P + 9 + r 
But, that p + q + r = o, and p z + q~ + ^ 
hath been already {hewn ; whence the truth of the 
general obfervation is manifeft. Hence it alfo appears, 
that the method of folution above delivered, is not only 
o-eneral, but includes this Angular beauty and advan- 
tage, that in all feries’ whatever, whereof the terms are 
to be taken according to the fame affigned order, the 
quantities (p> q, r, &c.), whereby the resolution is 
performed, will remain invariably the fame. The 
o-reater part of thefe quantities are indeed imaginary 
ones ; and fo likewife will the quantities be that re- 
fult from them, when fubflitution is made in the 
given exprefiion for the value of S. But by adding, 
as is ufual in like cafes, every two correfponding va- 
Vot. 50. jE lues > 
